| Quellen | Ich bin in Mathe so eine ziemliche Null, aber vielleicht gibt es unter euch das eine oder andere Ass? Bitte, ich bin echt darauf angewiesen! :/
Folgendes wäre ins Deutsche zu übersetzen:
"The functional equation of the Riemann Zeta Function, which is that: two to the power of one minus Z, times the gamma of Z, times the zeta of Z, times the cosign of a half pi Z, is equal to pi to the power of Z, times the zeta of one minus Z. The Gamma Function of Z is defined as: the integral between zero and infinity, of e to the minus t, times t to the power one minus z, integrated with respect to t- between zero and infinity. And that is also equal for a complex variable to Z minus one factorial. And the zeta function of Z is defined as the sum from n equals one to infinity of on over n to the power of Z. This functional equation is defined for Z being a complex variable, in other words, z equals x plus i y, where i is the square root of minus one. Now if we put z equal to two into this equation we already know that the zeta function of two is pi squared over six, so we get that: two to the power of one minus two, times the gamma of two, times the zeta of two, times the cosign of a half, pi, two. A half of two is one so we have the cosign of just pi s equal to pi squared, times the zeta of one minus 2.
Therefore, two to the power of minus one, times the gamma of two, we know the gamma function here is being z minus one factorial, so two minus one- one factorial is just one time one, which is one… times- we know that the zeta of two is pi squared over six and we know that the cosign of pi is minus one equals pi squared times the zeta of minus one. Bringing this all together: we know that two to the power of minus one is a half, so you have a half times one, so just a half, times pi squared over six, so a half times a sixth is a twelfth times minus one, so we've got minus pi squared over twelve which is equal to pi squared times the zeta of minus one. And now if I divide both sides of the equation by pi squared, it goes, minus a twelfth equals the zeta of minus one. And we know from here that the zeta function of z is; one over n to the z, where n goes up to one, two, three, four, five, six, so the zeta of minus one will be one over one to the minus one, plus one over two to the minus one, plus one over three to the minus one, plus one over four to the minus one, plus one over five to the minus one up to one over infinity to the minus one. So we've got one to the minus one is just one, two to the minus one is a half, three to the minus one is a third, four to the minus one is a quarter, five to the minus one is a fifth- so one divided by one is one, one divided by half is two, one divided by a third is three, one divided by a quarter is four, one divided by a fifth is five , up to one divided by an infinitieth which is infinity equals minus a twelfth."
Ich werde es selbst natürlich auch versuchen und dann posten. Ich bin noch nicht bei dieser Stelle angelangt, aber habe gesehen, dass sie noch auf mich zukommt. Wäre dringend... :/ |
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